Problem: Express this product in scientific notation: $(4.80\times 10^{-2})\times (8.00\times 10^{4})$
Answer: Start by collecting like terms together. $= (4.80\times 8.00) \times (10^{-2}\times 10^{4})$ When multiplying exponents with the same base, add the powers together. $= 38.4 \times 10^{-2\,+\,4}$ $= 38.4 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $38.4$ is the same as $3.840 \times 10$ $ = {3.840 \times 10} \times 10^{2} $ $= 3.840\times 10^{3}$